been struggling this whole day with trying to figure out the multiplicative inverse of 17 modulo 31. I know by "manual" computation that the actual inverse is 11 but how do I prove this with Euler's theorem. We know that 31 is a prime, φ(n)=30, so i end up with 17^30=(cong)1 (mod 31). But how do proceed from this? Would be very thankful if someone could help me out since im stuck. Thanks in advance.
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1What does this question have to do with programming? You need to check the [help]. – Kyll Aug 17 '15 at 17:06
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this belongs at http://math.stackexchange.com/ ? – trooper Sep 10 '15 at 20:43
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Well, lets formalize it. Lets a = 17, p = 31, you want to find a^(-1). So we get by Euler's theorem a^(p - 1) = 1(mod p). Lets divide both parts by a: a^(p - 2) = a^(-1) (mod p)
Answer: 17^29 (mod 31)
Valery Stromov
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